Painlev\'e analysis for the cosmological field equations in Weyl Integrable Spacetime

TL;DR

This paper uses Painlevé analysis to study the integrability of cosmological field equations in Weyl Integrable Spacetime, revealing conditions under which solutions are analytic and expressible as Laurent expansions.

Contribution

It demonstrates the Painlevé property of the gravitational equations in Weyl spacetime with a cosmological constant, providing explicit analytic solutions.

Findings

Field equations possess the Painlevé property with a cosmological constant.

Analytic solutions are expressed by a left Laurent expansion.

Integrability depends on the presence of the cosmological constant.

Abstract

We apply singularity analysis to investigate the integrability properties of the gravitational field equations in Weyl Integrable Spacetime for a spatially flat Friedmann--Lema\^itre--Robertson--Walker background spacetime induced with an ideal gas. We find that the field equations possess the Painlev\'e property in the presence of the cosmological constant and the analytic solution is given by a left Laurent expansion.